nLab Szpiro's conjecture

A statement about elliptic curves.

Relation to other statements

In its general form, equivalent to the abc conjecture.

If Mochizuki's corollary 3.12 is true, then Szpiro’s conjecture is also true.


The relation to the abc conjecture is discussed in

  • Matt Baker (notes taken by William Stein), Elliptic curves, the ABC conjecture, and points of small canonical height (pdf)

The relation to Mochizuki's corollary 3.12 is discussed in

  • Taylor Dupuy, Anton Hilado, Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki’s Corollary 3.12, (arxiv:2004.13108)

Last revised on June 21, 2021 at 15:58:25. See the history of this page for a list of all contributions to it.